A Comparison of Some Methods for Parameter Estimation in the Mixed Lognormal Distribution

The use of the lognormal distribution in reliability and maintainability analysis has become increasingly widespread. This paper deals with estimating parameters from a mixture of two lognormal distributions. First, quasi moment estimation is used to estimate the mean and reliability of the mixed model when data are grouped and Type-I censored. Second, maximum likelihood estimation is used to estimate the parameters. Third, plug-in estimation is used to estimate the parameters. Finally, presented is the mean square error and bias for each estimation of the parameters of a mixed lognormal distribution. Simulation study of the estimator has been carried out by two method, normal equation and the steepest descent method through Monte Carlo simulation.